If your Audi TT idling roughly, it could be caused by many things. Principally, the engine will show a rough idle if there are issues with the air-to-fuel ratio of the engine, or if there are problems with the ignition system. The malfunctioning parts may vary between TT model years and trim levels, which have offered a few different engine options throughout its production.
Check the spark plugs and ignition coil packs that sit above each spark plug. You can access this part of your TT's engine by opening the bonnet and removing the plastic engine cover. If the plugs are covered in soot and look dirty, or if any of the ignition coils do not fire while the engine's running, this could be the cause of your rough idle.
Use a fuel injector cleaning solution that can be poured into your Audi TT's gas tank. These chemicals help dissolve dirt and contaminants that could be hindering the flow of fuel into your TT's cylinders. Typically, the fuel injector cleaner is poured in when there is approximately 1/4 tank of gas left.
Check intake manifold and its associated parts including the idle control valve, air box, air filter, and hosing. If the hosing is cracked, there could be too much air being sucked into the intake manifold, thus causing it to run roughly. As the engine runs, follow the components attached to your TT's intake manifold and listen for hissing, which can indicate leaks in the intake system.